Surface formula identification

[sapiental]

Homework Statement

Identify the surface given by the equation 4x^2 +4y^2 −8y −z^2 = 0.

Homework Equations

x^2/c^2 + y^2/c^2 - z^2/c^2 = 1

(textbook definition for hyperboloid of one sheet.

The Attempt at a Solution

I know just by looking at the textbook formula what surface this is. However, my professor gives the following answer for the problem..

It is a hyperboloid of one sheet, x^2 + y^2 − z2/2^2 = 1

I get what the surface is, I just don't understand how he algebraically changed the formula to the above solution..

is (4x^2 +4y^2 −8y −z^2 = 0 ) the same as (x^2 + y^2 − z2/2^2 = 1)?

thanks. :)

 

[benorin]

complete the square on the y term.